In this paper, a new analytical approach is proposed for free vibration and buckling analysis of a rectangular Mindlin plate resting on the Winkler–Pasternak foundation of varying stiffness. According to Mindlin theory, there are three independent governing differential equations. Thus, three Fourier series expansions along with auxiliary polynomial functions are employed to represent the plate’s deflection and rotation angle functions. The process of making a set of equations is then completed satisfying the corresponding equilibrium equations and boundary conditions. The proposed method incorporates general elastic supports for all plate’s edges, and subsequently can deal with all possible boundary conditions including classical ones as well as uniform or non-uniform elastic constraints. The natural frequencies and buckling loads of several examples are determined to merely show the accuracy of the presented approach.

在本文中，提出了一种新的解析方法，用于对刚度不同的Winkler-Pasternak基础上的矩形Mindlin板进行自由振动和屈曲分析。根据Mindlin理论，存在三个独立的控制微分方程。因此，三个傅立叶级数扩展和辅助多项式函数一起用来表示板的偏转和旋转角函数。然后满足相应的平衡方程和边界条件，完成了一组方程组的处理。所提出的方法为板的所有边缘合并了通用的弹性支撑，并且随后可以处理所有可能的边界条件，包括经典条件以及均匀或不均匀的弹性约束。确定了几个示例的固有频率和屈曲载荷，仅显示了所提出方法的准确性。